Summary of "MATH 6 QUARTER 1 - WEEK 2 || MULTIPLIES SIMPLE FRACTIONS AND MIXED FRACTIONS"

MATH 6 — Quarter 1, Week 2: Multiplying Simple Fractions and Mixed Fractions

Main ideas / lessons

Multiply numerators together and denominators together, then simplify the result.
Convert mixed numbers to improper fractions (and vice versa) when needed before multiplying.
Use cancellation (cross-reduction) before multiplying to simplify arithmetic and often produce the product already in lowest terms.
Types of multiplication you will encounter:
- fraction × fraction
- fraction × whole number (treat whole as over 1)
- fraction × mixed number (convert mixed to improper)
- whole number × mixed number
- mixed number × mixed number (convert both to improper)
Multiplication can be written using ×, ·, parentheses, or words such as “times,” “product of,” “multiplied by,” or “of.”

Methodologies and step-by-step procedures

1. Multiplying two fractions

Multiply the numerators to get the new numerator.
Multiply the denominators to get the new denominator.
Simplify the resulting fraction (reduce to lowest terms). If it is improper, convert to a mixed number if required.

2. Cross-cancellation (recommended before multiplying)

Look for common factors between any numerator and any denominator across the fractions.
Divide the numerator and the matching denominator by their greatest common factor (or a convenient common factor) to reduce them.
After all possible cancellations, multiply the remaining numerators and denominators.

Benefit: This simplifies arithmetic and often yields a fraction already in lowest terms.

3. Converting mixed numbers ↔ improper fractions

Mixed → Improper:
- Multiply the whole number by the denominator, add the numerator, place over the original denominator.
- Example: 3 1/2 → (3 × 2 + 1) / 2 = 7/2.
Improper → Mixed:
- Divide the numerator by the denominator. The quotient is the whole number; the remainder is the new numerator; the denominator stays the same.
- Example: 24/5 → 4 remainder 4 → 4 4/5.

4. Multiplying when one or both factors are whole numbers or mixed numbers

Treat whole numbers as a fraction over 1 (e.g., 8 → 8/1).
Convert mixed numbers to improper fractions, then proceed with fraction × fraction multiplication and simplify.
Typical flow:
1. Convert mixed numbers to improper fractions.
2. Cancel across numerators and denominators if possible.
3. Multiply remaining numerators and denominators.
4. Convert an improper result to a mixed number if needed.

Notation alternatives

You may see multiplication written as:

1/2 × 3/4
1/2 · 3/4
(1/2)(3/4)
In words: “one-half times three-fourths,” “the product of one-half and three-fourths,” or “one-half of three-fourths.”

Representative example problems and solutions

Basic fraction × fraction (Learning Task 1)
- 3/4 × 1/2 = 3/8
- 1/5 × 3/7 = 3/35
- 8/11 × 7/9 = 56/99
- 5/13 × 6/7 = 30/91
- 8/17 × 4/5 = 32/85
Using cancellation before multiplying (Learning Task 2)
- 4/5 × 10/11: cancel 5 & 10 → (4/1) × (2/11) = 8/11
- 7/9 × 18/25: cancel 9 & 18 → (7/1) × (2/25) = 14/25
- 18/15 × 9/24: multiple cancellations → result 1/5
- 9/16 × 6/9: cancel 9 & 9; reduce 16 & 6 by 2 → (1/8) × (3/1) = 3/8
- 18/25 × 8/27: cancel 18 & 27 by 9 → (2/25) × (8/3) = 16/75
Fraction × whole number and mixed numbers (Learning Task 3)
- 3/5 × 8 = 24/5 → 4 4/5
- 5/6 × 3 1/2: convert 3 1/2 → 7/2; (5/6) × (7/2) = 35/12 → 2 11/12
- 6 × 5/12: treat 6 as 6/1; cancel 6 & 12 → (1/2) × 5 = 5/2 → 2 1/2
- 7 1/8 × 24: convert 7 1/8 → 57/8, then cancel with 24 as possible before multiplying
- 4/9 × 27 × 1/2: cancel 9 & 27; cancel 4 & 2 → final result 6
Mixed × mixed and multi-factor products
- 8 2/5 × 18 1/3: convert both to improper, cancel common factors across numerators and denominators, multiply → example produced 154 (i.e., 154/1)
- 6 × 2/3 × 2 1/2: convert 2 1/2 → 5/2; cancel (6 and 3 by 3, etc.) → final product 10
More practice with cancellation (Learning Task 4)
- 5/7 × 14/35: cancel 5 & 35 → 1/7; cancel 7 & 14 → 2/1; result 2/7
- 4/5 × 10/11: cancel 5 & 10 → (4/1) × (2/11) = 8/11
- 8 3/4 × 2/9: convert 8 3/4 → 35/4; cancel 4 & 2 → (35/2) × (1/9) = 35/18 → 1 17/18
- 4/5 × 10/11 × 7/8: perform similar cancellations → result 7/11 in the example

Note: The video consistently emphasizes canceling common factors across numerators and denominators before multiplying to keep numbers small and to produce simplified answers more easily.